A Novel Pulse Designed to Jointly Optimize Symbol Timing Estimation Performance and the Mean Squared Error of Recovered Data

A new optimal pulse is derived considering both the symbol timing estimation performance and the mean squared error of intersymbol interference corrupted data recovered in timing error. The new pulse design minimizes the mean squared error of the recovered data averaged over the timing error, accounting for the fact that the distribution of the timing error is also affected by the pulse shape. The new pulse resembles the Franks' double-jump pulse, but has different slope than the Franks' double-jump pulse in the spectral rolloff region. Although the new pulse has greater mean squared error than the Franks' pulse for a fixed small timing error, it has better symbol timing estimation performance and better overall performance as measured by the Cramer Rao lower bound and by the mean square error of the recovered data accounting for both timing recovery effects and data recovery distortion, respectively. An optimal pulse that minimizes the mean squared error of intersymbol interference corrupted data recovered in the presence of fixed but arbitrary timing error is derived as an intermediate result.